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If 2 is a root of eq xsquare+kx+12=0 and eq xsquare+kx+q=0 has equal root.find the value of q

Since 2 is a root of x2+kx+12=0So, 2 will satisfy this equation.22+(2)k+12=0⇒4+2k+12=0⇒2k+16=0⇒2k=-16⇒k=-8Now, given x2+kx+q=0 has equal roots.So, Discriminant,D=b2-4ac=0    where a=1,b=k and c=qk2-4q=0⇒(-8)2-4q=0⇒64-4q=0⇒4q=64⇒q=16

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As 2 is a root of x2 + kx + 12 = 0 then it must satisfy it
therefore :  (2)2 + k (2) + 12 = 0
             => 4 + 2k +12 = 0
            =>  k = -8    
now using the value of k in the second equation
x2 + (-8)x + q = 0

this equation has equal roots, say a and a
so   2a = - (-8)/1
 => a = 4

now,  q = a2
   => q = 16

ANSWER = 16

 
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